The phrase often reflects a personal feeling or opinion, so it may vary from person to person. I don't feel up to going out tonight, but you might have enough energy.
Pro Tip 2/3
Not Obligatory
'Feel up to' implies a choice based on one's condition, rather than a requirement. Let me know if you feel up to trying that new dance class, but no pressure.
Pro Tip 3/3
Emotional State
Can also refer to an emotional readiness, not just physical or mental ability. After the breakup, she didn't feel up to attending the party.