In a Breadth First Search (BFS) traversal of a graph, you traverse all vertices at one level before moving on to the next level.
You start by traversing from any vertex say currentVertex. If adjacent vertices to the currentVertex are not yet visited then print their value. Then repeat the same for children of the currentVertex.
In a Depth First Search (DFS) traversal of a graph, you traverse the vertices depth wise rather than breadth wise. You start by traversing from any vertex say currentVertex - pick any one of it's adjacent vertex and keep traversing adjacent vertices until the farthest vertex is reached. Then you move back to the starting vertex and repeat the same for another adjecent vertex. You repeat this process until all the vertices are traversed.