Traditional career paths post post-doc I am in the process of submitting my PhD thesis, and have been offered a 1yr post-doc role at my current institution. If it matters, I am in UK and work in applied mathematics at a well-known faculty.

My question relates to "traditional" career paths after the initial post-doc, or more specifically what are good reasons (or the only reason) for embarking on post-doc research? The reason I am asking this question is because I switched from industry (after 5 years experience) to research in order to carry out my PhD, which happens to be on a topic relevant to both industry and academia. So I have come to research and academia in a bit of a backwards way.

Like many other researchers, I found thesis work hard-going and throughout much of my PhD assumed I would simply slip back into industry after completion. But as my thesis began to reach the closing stages, and I reflect upon my work, I realised that there are numerous aspects of research that I genuinely enjoy, and value. But I do not know if this is a good enough reason to continue with post-doc research. 

Thinking beyond my current offer, during my investigations for post-doc roles I have been struck by how transient, or temporary, many roles are (at least in my area). So my question is what are the traditional "end goal(s)" of a series of temporary post-doc positions? Am I correct in thinking that I should only be doing this if I fully intend on seeking a full-time salaried academic position? How long does this take, and what is the "success rate" of post-doc to full-time academic?

The thought of job-hunting every year, or few years, for the next X years seems quite...daunting. And I worry that if there is a high chance I will return to industry in X years time (for whatever reason) - then I probably need to factor that in to my decision making now.
The reason to do a postdoc is because you want to continue to do academic research.  This might be a short-term goal, or a long-term goal, or exploratory (you're not sure what you want to do long-term).  The latter two are the usual reasons.

Lots of people go into industry after doing postdocs (either because they decided they prefer that or couldn't find an academic job they wanted), so that's no issue.  Keep in mind that it's generally easier to go from academia to industry than industry back to academia.

How long it takes to transition from post-doc to a permanent faculty position depends on the field and type of job you want.  In math, 3-4 years (1-2 postdocs) is normal before getting a permanent research job and 0-3 is common for moving into primarily teaching jobs.

As for "success" rates from postdoc to permanent faculty, I think they're reasonably good, say over 50%.  I quoted some relevant data from the AMS in this answer, though I don't think the right data is there to give you a precise number.  If you take into account that a large fraction of these people want to leave academia, the success rate should look quite good.