In many cases, the Three of Cups comes up in relationships readings when there is a third person involved. Often time, you are that third person dealing with an unfaithful partner.
When this card appears in a reading, look at the other cards for more details on the nature of the relationship. If you see the Seven of Swords, there is possibly a betrayal of trust and cheating; if you see the Five of Swords, it is likely that you already know about the other relationship but you are trying to ignore it; if you see the Devil, think carefully about the nature of the relationships as they are likely to be harmful for those involved.
On a broader scale, the reversed Three of Cups can indicate the limitation to your creativity because you are forced to settle with the group in which you are. You might be part of a group that does things in a certain way and is closed to innovating or alternatives. You should consider if you are willing to sacrifice your creative abilities for the group desires.
This card may reflect an isolation from other people. Should this be the case, take charge of this problem and reconnect.
Following the same idea, the Three of Cups reversed might state that you have lost touch with your friends, probably because of other priorities like work or family. It is good to see this card as a reminder to get back in touch with them, have a good time and do not worry too much about consequences.
On the other hand, the Three of Cups reversed may indicate excess in the party scene. Maybe you are spending too much time outside at bars. Take into account the long-term consequences and ask yourself if you are living a sustainable life. Take a break, regroup and get some sleep.