The ATLAS detector
The ATLAS (A Toroidal LHC ApparatuS) detector is one of the four gigantic particle detectors which have to measure the results of the high-energy interactions produced when the particles (protons and heavier nuclei) accelerated by the CERN Large Hadron Collider (LHC) are forced to collide.

Keep your eyes on what happens in the control room.
What happens during particle collisions?
Because the incident particles have very high energy (7 TeV each; 1 TeV = 1000 GeV) compared to their rest energy (given by c2 multiplied for their masses: ~ 1 GeV for protons, and ~A GeV for nuclei with mass number A), a number of secondary particles are produced as a result of their interaction.
Einstein found at the beginning of the XX century that mass and energy are connected (everybody has seen his most famous equation E = m c2) in such a way that it comes out to be possible to convert mass into energy and vice versa. This is exactly what happens during the collisions induced at the LHC ring: part of the total initial energy (14 TeV) is converted into mass (plus kinetic energy) of a number of secondary particles, most of which have a short life time (i.e. decay into different and lighter particles). These secondaries fly away from the interaction point, usually leaving "signatures" of their passage through the detectors which are built around the interaction point.
Only few particles escape the detector without leaving track of their passage: they usually are neutrinos, the extremely light neutral companions of the charged leptons (see my physics page for more details). Of course, other particles may not leave track of their passage, for example if they deposit a very small amount of energy (below the minimum detectable threshold), or if they cross the detector "dead material" (the zones in which there is no detector at all). But don't worry: these zones are so small that they are usually named "cracks", even if there is no break at all!
In addition to known particles like neutrinos, other exotic particles (not described by the particle Standard Model) may exist which would leave no track at all in the detector, for example the neutralinos foreseen by supersymmetric models. Actually, finding new particles is one of the main goals of the four LHC detectors.
How can we see the secondary particles?
Charged particles leave (part of) their energy on the detector active materials, which react to this energy deposition in some way and are coupled to electronics able to amplify and record this signal. If one takes the "spots" left on different parts of the detector, he is able to find the trajectory followed by different particles, thanks to intensive computer tasks. In addition, the deposited energy is a function of the particle charge, which can be reconstructed this way.
The strong magnetic field of the ATLAS detector makes charged particles follow curved trajectories: by measuring the curvature radius and the bending direction it is possible to know their momentum and charge sign, respectively. At the end, we are able to say that a given track was produced for example by an electron with 30 GeV kinetic energy.
Actually, this reconstruction is possible only when the secondary particles are traveling not too parallel to the initial particles direction, because the detectors must have holes to let them enter! Usually, the best detection region is around the plane perpendicular to the LHC vacuum tube, which lets the incident particles enter the detector, passing through the interaction point, known as "transverse plane". Often, one projects on this plane the measured quantities and speaks, for example, about the "transverse momentum".
How can we decide what events shall be recorded?
The initial ATLAS interaction rate will be ~40 MHz (~1 GHz at full LHC luminosity) and it is impossible to keep record of all events. Actually, it is also useless: most of them will not teach us anything new. Hence a selection must be done, which discards most of the events still keeping those potentially interesting for us.
The digital signal which says to the electronics "OK, save the event information!" is called trigger and, by analogy, the logics behind it are collectively called "trigger". Hence, the trigger of an experiment is the part which takes decisions about event selection.
The ATLAS detector has a trigger system divided into three levels: the "first-level trigger" (L1) is hardware based and must reduce the interaction rate to at most 75 kHz. Hence L1 discards 99.9% of all events; the "second-level trigger" (L2) must reduce the event rate to about 1 kHz, by discarding 99% of all events which passed the L1 selection; finally, the "event filter" (EF) has to further reduce this number a factor of ten, saving on disk events with a rate of about 100 Hz. Both L2 and EF, collectively known as "high-level trigger" (HLT), are implemented as big farms of computers to which events are distributed in order to take profit of their parallel execution.
What events are to be considered interesting?
In principle, all events which have a large fraction of energy released on the transverse plane are potentially interesting. Still, the LHC event rate is so high that one has to discard most of them and retain only selected categories of events. For this reason, a table of possible interesting signatures is being used to take the trigger decision. For example, one will want to record all events with large missing transverse momentum, because this is what it is expected to happen when new particles called neutralinos (present in supersymmetric theories) are produced.
Useful links
The ATLAS detector has extensive documentation in the form of TWiki pages. They are quite detailed and complex: an important (alternative) starting point could be the alphabetical index of all TWiki pages. Another very good page is the list of the ATLAS acronyms. The general reader may find useful to check the CERN and Fermilab web pages.