Crossed aldol condensation is a variation of aldol condensation.

aldol condensation:

crossed aldol condensation:

eg:

Mechanism:
Step 1:  The hydroxide ion deprotonates the enolizable aldehyde reversibly.

Step 2:  Enolate ion 1 preferentially adds to the non-enolizable aldehyde, which has the sterically less hindered and, therefore, more accessible carbonyl carbon.

Step 3:  Alkoxide ion 2 is protonated by water.

Step 4:  Aldol 3 is an enolizable aldehyde.  A small amount of it is converted to the corresponding enolate ion (4) by the hydroxide ion.

Step 5:  Enolate ion 4 loses a hydroxide ion.

Step 1 through 3 are a crossed aldol reaction, steps 4 and 5 a 1,2-elimination via E1cB mechanism.  Thus, crossed aldol condensation is crossed aldol reaction followed by 1,2-elimination.