A tissue is basically a collection of cells which are gathered together for a particular function. Because a cell is like the bricks which make up living beings, you could think of a tissue like the wall which is made out of cells. In other words, if you get a collection of the same kind of building blocks together, you get what we call a tissue.
There are lots of different kinds of tissues, and each of them may be made up of slightly different cells. But ultimately a tissue is where you get a collection of cells for one particular function. An example of a tissue is a collection of muscle cells. When you get a collection of muscle cells, they can work together to cause contraction.
The body is made up of lots of tissues, which are collected into specific organs. You may hear people talking about 'transfering oxygen to the tissues', or 'damage to the tissues'. It's just a helpful way of talking about collections of cells in particular places or around the body - not just individual cells, but collections of cells.
If a tissue is a collection of cells, then an organ is a collection of tissues. Even though each tissue is specially designed to perform a specific function, you often need a few tissues together in order to achieve a particular overall task.
For instance, the heart needs to get blood around the body. It does this by contracting, squeezing blood through valves which stop the blood from flowing backwards. If we were to just think about these two things, there are already a number of functions that we need to achieve. We need muscles to contract, so we need the muscle tissue (in this case, we call is the myocardium). Then we also need tissue which doesn't contract to form the heart valves. We also need a packaging to contain it all, and we need special tissue to make sure the signal to contract is transmitted across the heart in the right way.
So an organ is a collection of tissues which are joined to achieve a particular purpose.
Sometimes you need organs to work together to achieve a bigger purpose. When these are all connected then they are called an organ system.
For example, the body needs to transfer oxygen from the lungs to the rest of the body. It has a specialised system to do this, called the circulatory or cardiovascular system. This is made up of the heart, the blood vessels and blood. Each of these work together to make sure that the oxygen (and a number of other things!) can be transported appropriately.
There are actually a large number of organ systems in the body, which work together to make sure that the things which the body needs to do can be done successfully. Any problem at any level, from cell to organ-system, can cause a problem which we notice as disease.