The most common way that people think of a gene being turned on is via transcription factors. Transcription factors are proteins that bind to specific sequences of DNA (e.g. TAATA), that are found in a "promoter region" before any specific gene. They also tend to be at the end of long and complex signalling pathways (think a circuit). Typically, this form of gene activation is considered separate to epigenetics.

Epigenetic modifications are things that allow transcription factors access to those specific promotor regions. For example, DNA methylation occurs on the promotor region, and blocks transcription factor access to the binding site, effectively silencing that gene.

Likewise, access to DNA by transcription factors is dependent on the structure of the histone. DNA wraps itself around histones like a hose around a spool. Histones can either become methylated or acetylated on specific parts that change that structure to deny/allow transcription factors access to the DNA.

This is very important in embryogenesis - once your brain cell has been programmed to be a brain cell, you don't want the heart cell DNA turning on, so certain histones are "locked" by epigenetic mechanisms.

Additionally, mutations to genes encoding the histones have found to be the cause (or one of) of multiple childhood cancers in the last decade, including most notably one of the deadliest brain cancers called Diffuse Midline Glioma. In this cancer, a histone gene is mutated such that one of the histones can't be turned off, so the cell remains in a progenitor-like cell state.