1To push or force something (or someone) into a space; to cram or stuff into.
スーツケースに洋服を無理やり押し込んだ。
I forced my clothes into the suitcase.
忙しい朝で、バッグに教科書を押し込んで家を出た。
On a busy morning I shoved my textbooks into my bag and left the house.
乗客たちは満員の電車に押し込まれた。
Passengers were shoved into the packed train.
2To force one's way in (into a house/building); in criminal contexts used for break-ins or burglaries (as in '押し込み強盗').
昨夜、近所で押し込み強盗が発生した。
Last night, there was a home-invasion robbery in the neighborhood.
犯人は窓を割って部屋に押し込んだと見られる。
It appears the perpetrator broke a window and forced their way into the room.
荷物を車の中に押し込んだ隙に、スリに財布を盗まれた。
While I was shoving luggage into the car, a pickpocket stole my wallet.