The data we get from the LHC is information about the particles that get created in the high energy collisions, information on particle properties such as particle energy, speed, mass and charge.
Imagine each collision is a suitcase. We then look inside a suitcase to see the clothing items, each different clothing item being a different particle, for example an electron is a left foot sock. We then look at the properties of each different clothing item such as colour, size and material.
What we’re most interested in finding is very rare particles (very rare pieces of clothing), such as the Higgs boson. The problem with rare particles is that they don’t live long. For example a Higgs boson only lasts for 0.0000000000000000000001s (22 zeroes!). So we don’t see a Higgs boson in our detectors, we only see the particles it breaks into. Imagine a Higgs boson was a Gucci jacket that got torn apart. We might find 2 sleeves of the same size, a collar and main body of the same colour and material. If these pieces fit together, we might conclude there was once a Higgs boson!
I don’t work with the LHC itself. I work as part of another facility at CERN called MEDICIS. It’s a new one which uses a high energy beam of protons to produce radioactive isotopes for medical research.