Mary was sad because she thought Jesus's body was taken ... but Jesus was still in the tomb. Only this time, Jesus was not lying down. Jesus then called Mary, and now Mary realized that she has seen Jesus -- resurrected from the dead!
Out of response from the newfound joy, Mary shouted, "Rabboni!" (translated as Teacher). She is really happy because Jesus countered death itself. In response to Mary's joy, Jesus told Mary to not "cling to [Him]" but rather "go to [His] brethren" and tell them about Jesus's future ascension (20:17). Based on Jesus comments, Jesus wants Mary to tell the disciples about Jesus, even though they were stuck in fear and helplessness. And Mary did just that!
Mary's testimony prior to the disciples re-meeting Jesus can serve as evidence for Jesus's resurrection because female witnesses are very unconventional (and would be very unlikely to be made up on the fly if this were made up). This is known as the "criteria of embarrassment". Cross Examined has many more great articles on Jesus's resurrection if you're interested (or still have questions).