Infiltration is a process where one of the squads is being sent to a location (with the "Go forth to stop EVIL" command). Most of the criminal activity the LCS performs in the game happens in the infiltration stage.
A successful infiltration can affect the public opinion of the issues associated with a location greatly, but infiltrating highly-secured areas is extremely dangerous. Some of the locations also have special tiles which can be used by the squad — for example, the cells in the Police Station and the Prison, the jury room in the Courthouse or the stage in the Cable News Station. Some locations also have loot spread around, which can be sold at the Pawn Shop after the infiltration.
If the squad has appropriate disguises for the location and has a high enough Disguise skill, they may get past the Conservatives successfully and get loot or use the special tiles without resistance.
Most of the criminal activities increase the squad's Juice, but performing them in front of moderate (not Conservative or Liberal) citizens may alienate the public and make the squad lose Juice. A lot of skills are also trained through infiltration.
A well-done infiltration may get the LCS into the newspapers. A violent infiltration may lower the public opinion on the LCS, so having someone who can write for the Liberal Guardian and put a positive spin on the events is likely to keep the LCS respected.
On the other hand, infiltrating a location can be extremely dangerous, getting your squad members injured or even killed in action. Liberals with the First Aid skill can stop others from bleeding to death during the infiltration.
If the Conservatives were alerted during the infiltration, they can pursue your squad even after it leaves the location. The possible options are to outrun the Conservatives, to kill them all in a fight or to give up and let them arrest or kill your squad.
Note: if you are in a high-speed car chase and there is a fruit stand ahead of you, always go straight into the fruit stand, and never swerve to avoid it (swerving to avoid it often results in your entire squad dying in a car crash).
Basically, during infiltrations, try to avoid having anyone killed or permanently injured, and try to avoid alienating everyone.