Liquids take the shape of their container due to the unique properties of their molecules. Unlike solids, which have a fixed shape because their particles are closely packed and vibrate in place, the molecules in a liquid are not held in fixed positions. They are close together but can move past each other freely.
This ability to move allows liquid molecules to spread out and fill the bottom of their containers. When you pour a liquid into a glass, for example, the liquid flows and conforms to the shape of the glass. If you were to pour that same liquid into a bowl, it would again change shape to fit the contours of the bowl. This behavior is largely due to the balance of cohesive forces (attraction between similar molecules) and adhesive forces (attraction between different substances) that occur in liquids.
In summary, the combination of the relative freedom of movement of liquid molecules, along with the forces acting between them, causes liquids to take the shape of whatever container they are in.