Solids in the periodic table are not all arranged the same. The common image of a metal or ionic structure has atoms layered on top of each other as below.
But most solids exist in a crystal structure. Crystals are repeating units, that happen over and over in the larger structure of a metal. These crystals are made up of atoms arranged in a 3D shape and have an allocated name for how they look. These 3D shapes are given names based on how the atoms are arranged and expand on our 2D understanding of how the atoms are arranged in a solid.
The 3D structure of a crystal is known as a unit cell. This is the repeating unit that is found over and over again in the 3D structure of a solid. The best way to imagine this is to treat atoms as spheres, whilst atoms are not perfect spheres it helps with imagery. If we stack the cannonballs in a pile there are only a certain number of ways we can stack them together, also there will be spaces between the cannonballs where they are not touching.
When we combine these units together they make the larger lattices of solids. A lattice is a large scale 3D collection of units. Not all units are the same however as there maybe imperfections in the structure and also they may be alloys where metal atoms of different sizes are packed together.
A crystal has a 3d arrangement of atoms highly ordered to produce 3d structures which have straight edges and flat faces
A repeating unit is a 3d shape which is copied and repeated over and over again exactly the same
Imperfections is the term used when a structure of a crystal or 3d material has crystals or units that are very different causing changes in the 3d shape
A lattice is a term given to an ordered arrangement of points in a 3D shape creating a regular arrangement of atoms and ions
A unit cell is a single unit of atoms that have the same overall symmetry and can be used to build up a total crystal lattice with the repetition of these units