Commitment is a word that, in everyday use, has a mostly positive connotation. We usually commit to change/help/fight and so on. It implies a (free) will to do something and the fact that the declared action should eventually take place. Well, when talking about climate, commitment is still something we expect to happen, but this is usually not the result of free will, rather an unavoidable consequence of past changes (Wigley, 2005).
In a nutshell, there is a quite clear relation between greenhouse gas concentrations in the atmosphere and global mean temperatures. The atmosphere responds very quickly to changes in forcing, hence the time-lag between concentration and temperature changes is rather short, with most of the warming occurring within less than a decade. This means that the positive effect of emissions reduction on global temperatures is rather fast: good and dangerous news at the same time, since it provides an easy argument to postpone emission cuts to the near future (e.g., in periods of economic crisis).
However, other components of the earth system, such as oceans, glaciers and ice sheets, take much longer to adjust to changes in forcing, from several decades for glaciers to thousands of years for ice sheets and deep-ocean warming: this is where the commitment issue comes into play. It can best be explained talking about sea level rise, which will have one of the largest impacts on populations worldwide. If temperatures rise, global mean sea level will also rise, because of thermal expansion and increased melting of glaciers and ice sheets. However, if temperatures rise today, glaciers and ice sheets will shrink and the ocean will warm up later this century, and they will keep doing so even longer. It implies that, even if we manage to limit global warming within a few decades, sea level will keep rising, because of the warming that has taken place in the past century and that will take place until we reach our climate targets. And this what scientist mean when they talk about climate change commitment: that amount of change that still has to occur.
Here, a few numbers, being aware of the fact that an accurate quantification of commitment is difficult, due to uncertainties in models and input data. A rather recent study (Clarke et al., 2018) predicts that even if we limit global warming to 2o C (i.e., the target of the Paris Agreement), global mean sea level will likely rise by 0.9 m at year 2300 and by 1.3 m at 2500 (2 m at 3000). In a quite possible – albeit more pessimistic – scenario, where global warming reaches 3-4o C later this century, the amount of rise would likely be 1.8 m by 2300 and 3.2 m by 2500 (6.5 m by 3000). In both cases, sea level will eventually rise by several (tens of) metres in the course of the following millennia.
So, this is why climate change commitment calls for timely climate action: every year we delay measures to limit greenhouse gas emissions will likely result in additional warming, and this will eventually cause additional changes in natural systems, e.g., further sea level rise. Maybe not this century, but surely for many centuries to come.
Wigley (2005), The Climate Change Commitment, Science, 307, 1766-1769, http://science.sciencemag.org/content/307/5716/1766
Clarke et al. (2018), Sea-level commitment as a gauge for climate policy, Nature Climate Change, 8, 648-659, https://doi.org/10.1038/s41558-018-0226-6
IPCC (2019), IPCC Special Report on the Ocean and Cryosphere in a Changing Climate [H.-O. Pörtner, D.C. Roberts, V. Masson-Delmotte, P. Zhai, M. Tignor, E. Poloczanska, K. Mintenbeck, M. Nicolai, A. Okem, J. Petzold, B. Rama, N. Weyer (eds.)], https://www.ipcc.ch/srocc/