Examples
Given the string foobarbarfoo:

bar(?=bar)     finds the 1st bar ("bar" which has "bar" after it)
bar(?!bar)     finds the 2nd bar ("bar" which does not have "bar" after it)
(?<=foo)bar    finds the 1st bar ("bar" which has "foo" before it)
(?<!foo)bar    finds the 2nd bar ("bar" which does not have "foo" before it)
You can also combine them:

(?<=foo)bar(?=bar)    finds the 1st bar ("bar" with "foo" before it and "bar" after it)

Definitions

Look ahead positive (?=)
Find expression A where expression B follows:
A(?=B)

Look ahead negative (?!)
Find expression A where expression B does not follow:
A(?!B)

Look behind positive (?<=)
Find expression A where expression B precedes:
(?<=B)A

Look behind negative (?<!)
Find expression A where expression B does not precede:
(?<!B)A

Atomic groups (?>)
An atomic group exits a group and throws away alternative patterns after the first matched pattern inside the group (backtracking is disabled).

(?>foo|foot)s applied to foots will match its 1st alternative foo, then fail as s does not immediately follow, and stop as backtracking is disabled

A non-atomic group will allow backtracking; if subsequent matching ahead fails, it will backtrack and use alternative patterns until a match for the entire expression is found or all possibilities are exhausted.

(foo|foot)s applied to foots will:
match its 1st alternative foo, then fail as s does not immediately follow in foots, and backtrack to its 2nd alternative;
match its 2nd alternative foot, then succeed as s immediately follows in foots, and stop.

Some resources
http://www.regular-expressions.info/lookaround.html
http://www.rexegg.com/regex-lookarounds.html

SRC:
https://stackoverflow.com/questions/2973436/regex-lookahead-lookbehind-and-atomic-groups