Uchikomi is the Japanese word for an invasion (qv).
The word is not much used in English in this sense, but it does occur in the book title Keshi and Uchikomi.
Uchikomi can also mean forcing an opponent to a (higher) handicap.
The uchikomi system was used before komi for White was introduced. (The komi in the word uchikomi is unrelated.)
Players of equal rank would alternate taking Black, a phase which was called tagai-sen. If one player was one rank weaker, that player would take Black two out of three times, this handicap being called sen-ai-sen. If the rank difference was even greater, one player would take Black all the time, which was called josen. Any further difference in rank was compensated by handicap stones. The name uchikomi means 'beating down'. This was based on the fact that in a series of games, if one player went four games up, he would 'beat down' his opponent to the next handicap level. Depending on the ranks of the players, a match on uchikomi terms could start with the weaker player at any particular handicap level.
For more information, see match handicap system.