An embedding is a list of numbers that captures the meaning of text. Two pieces of text that mean similar things will have similar numbers. That's it. That's the entire concept.
"How do I reset my password?" → [0.12, -0.45, 0.78, 0.33, ...]
"I forgot my login credentials" → [0.11, -0.43, 0.76, 0.31, ...] ← similar!
"What's the weather today?" → [0.89, 0.12, -0.34, 0.56, ...] ← different!
These number lists (vectors) typically have 256 to 3072 dimensions. More dimensions = more nuance = more storage = slower search.