Characteristics of the IBM quantum computer

A quick and dirty list:

• $T_{1}$ and $T_{2}$ - colloquially known as decoherence times, but slightly more precisely also as the (qubit) relaxation time ($T_{1}$) and the (qubit) dephasing time ($T_{2}$).
• $T_{1}$ is a measure of how quickly a qubit in the excited ($|1rangle$) state spontaneously relaxes to the ground ($|0rangle$) state.
• $T_{2}$ is slightly more tricky: it is a measure of how fast a coherent superposition (one with a well-defined relative phase between the $|0rangle$ and $|1rangle$) loses this 'well-defined-ness'. Essentially, it's what makes a qubit a quantum phenomenon; a (completely) dephased qubit is just a probabilistic classical bit.
• Frequency - the qubits from IBM are superconducting qubits. Interactions with these qubits are performed via microwave resonators; to address each different qubit separately each' qubits resonator has a different frequency. As @Lena has pointed out, the frequency is actually defined as the energy difference between the $|0rangle$ and $|1rangle$ states.
• Readout assignment error - measure of how well the measurement performs - as luciano mentions in his answer, the probability of a measurement returning the wrong value.
• Prob meas0 prep1 - The probability that a measurement returns $0$ immediately after preparing the $|1rangle$ state. A combination of faulty preparation and faulty measurements; these are also often referred to as SPAM (state-preparation-and-measurement) errors.
• Prob meas1 prep0 - like the previous one
• Readout length (ns) - time it takes to perform a measurement in (ns). One of the main limiting factors of current quantum hardware; as these times are often considerably longer than the $T_{2}$, which makes intermediate measurements (i.e. measurements that are not at the end of a circuit) practically unfeasible.
• ID error - measure of the error induced by having the qubit idle (for a typical gate time). The measure used is, I believe, that 'returned' by randomized benchmarking, which closely resembles the process fidelity.
• $sqrt{X}$ error - measure of error induced by applying the gate in question. Average over all different qubits.
• Single-qubit Pauli X error - likewise
• CNOT error - error of the only two-qubit gate natively implementable on the IBM devices. Average over all possible CNOT gates
• Gate time (ns) - Lena to the rescue again - this is related to the time it takes to perform a CNOT, the two-qubit gate.

And why isn't there, for example, a Pauli-Z error, even though there is a Pauli-X error?

The reason there is no error shown for the Pauli Z is because there is (virtually) none. This is because the IBM machines don't really implement $Z$ rotations - they keep track of the $Z$ rotations through software, and update the $X$ (and $Y$) gates accordingly. Effectively, they rotate the $X$ and $Y$ axes of the Bloch sphere along the $Z$ axis - the 'Pauli X' gate is thus actually any rotation along an axis in the $X-Y$ plane of the Bloch sphere. By changing the phase of the induced wave on the resonator, one can pick the angle the axis makes with a predetermined reference point, and thus implement both $X$ and $Y$ gates.

You might also find this page on system properties and this qiskit notebook on calibration useful.