You can select food that is healthier. Most batch- or mass-cooked food is of the minimal quality permitted, and is often cooked or fried, as this is the simplest and one of the cheapest ways to do so. You can also tailor-fit the food to your requirements, whether they be for religious, ethical or health reasons.
You can take a lot and eat it all if you are hungry, or save some for later. This means you don't spend money on buying something when you know you will throw half of it away.
It can be cheaper. Getting a multipack of what-have-you and using one each day for two weeks will usually cost less than buying one every day for the same period of time. The same goes for bulk foods like fruit and vegetables, bread and meat for Sandwiches, etc.
You can choose what you will have. You can get up in the morning and decide on a couple of options for what you feel like on that day if you aren't sure exactly what you might like at the time, or just fill your bag or lunchbox with your favourites.
The quality is usually higher. You can individually pick the best Apples from the cart in the store, put the ideal amount of spread in your sandwich, pick the flavour of juice or milk in the shop, and many other such things, to create the best meal for you, rather than relying on frozen/stored fruit, low quality spreads and little of it, and the blandest cheapest available drinks.
It is much easier to keep track of a named item like a lunchbox than it is to protect a pocketful of small change.
