To place one's body against another person's, with little or no arm-wrappage.
A gesture similar to a hug, with lack of effort and/or passion.
Phyllis: How was your date with Tom?
Pam: It was great until he body pressed me.
To place ones lips on another person, without puckering.
A gesture similar to a kiss, but lacking effort and/or passion.
Jim: I saw you kissing my girlfriend, Jack.
Jack: No worries Jim, it was just a lip press.