"Your Offset" is the offset you set for the beatmap specifically. This can be done with the + and - keys. It's generally recommended to leave it at 0 unless you feel that the map's offset is incorrect. This is also known as the Local Offset.
"Online Offset" is the offset set by a QAT (or GMT, if I recall correctly). It's basically used if the map has an incorrect offset but has already been ranked. This way the map gets played at the correct offset (in multiplayer for example) without the user having to manually adjust it.
In both cases the offset basically pushes the hit objects back in relation to the song by the amount entered in miliseconds.
And while this wasn't in your question: You also have Universal Offset. This can be found in the options menu. This offset pushes all audio back by the amount entered in miliseconds.
All offsets are used to sync the audio with the beatmap.
