Though they both have a similar meaning, there is a subtle difference. Both can mean 'to attend, to participate, to take part in.'
The difference is that 参加 carries the meaning of attending the event as a spectator or simply being there, while 参与 carries the meaning of actually taking part in the event.
Let's look at an example sentence: "我下周六要去参加我朋友的婚礼。I'm going to attend my friend's wedding next Saturday." The use of 参加 here implies that you are going to the wedding and will probably sit among the guests and witness it. If we replace 参加 with 参与, it would imply that you are going to the wedding, but you have a role in the events, such as being part of the wedding party.
One more sentence to clarify: “他昨天晚上参与足球比赛。Last night he played in the soccer game." Here we can translate 参与 as 'played' because it is implied that he participated in the match. If we said 参加 instead, it would mean that he was present at the game, but as a spectator. Therefore we'd translate it as 'Last night he went to the soccer game.'
Hope this helps. Have a nice day : )