A detector is an assertion that some set of measurements has deterministic parity under noiseless execution. A detector produces a detection event when this parity is different from what was expected. The most common form of detector is a pair of measurements measuring the same stabilizer, one after the other.
Is the detection events mean that temportal and spatial coordinates that errors happens?
Detection events are not coordinates. Strictly speaking, detection events don't even need to be associated with coordinates at all. Detection events come from combining information from different times and places, so they span a region of space and time. That said, it's convenient to give them some sort of coordinate so that you can easily refer to them. For example, you could set a detector's coordinates to the average of the coordinates of the measurements in its set of measurements.
In a stim circuit, you can assign coordinates to a detector by annotating them as parens arguments:
# this detector's coordinate data is set to x=1, y=2, t=3
DETECTOR(1, 2, 3) rec[-1] rec[-2]
This information has no effect on simulations, or on decoding of errors, it's only used for things like diagrams and debugging.
after finding my detection events, how can I use this structure to decode/matching in pymatching?
You would typically give the detection events to pymatching.Matching.decode as either an array of bits (one for each detector, with 0 for no detection event and 1 for yes detection event) or as a list of ints with each int indicating a bit positions where there would be a 1 instead of a 0.
The order of the bits comes from the way you defined the pymatching.Matching. For example, if you created it from a stim detector error model or circuit then it matches the order of detectors from the detector error model or circuit.
