We talk a lot about Agile teams being cross-functional or multi-disciplinary, but in Agile we need to be careful that we encourage one type of team, and not the other, and that we understand the difference between the two terms.
So...what IS the difference?
In my opinion, A multi-disciplinary team (MDT) is a team made up of a group of people who hold different disciplines. People in multi-disciplinary teams tend to by I-shaped. That is, they have a very deep expertise in a specific area, but much less breadth across other skill areas.
What Agile teams do best with is T-shaped people. T shaped people also have specialties - a strong depth of skill in a given area - but they also have skills (breadth) spread across other areas of the team's knowledge work, too. Just like the uppercase 'T' - depth and breadth of knowledge.
In Agile teams, and especially in Scrum, cross-functional teams are critical to success. Cross-functional teams have all of the skills needed to get the work done, with plenty of skills overlapping to reduce the dependency on the skills and expertise of any one team member. Work, and consequently the 'success' of the team, in Scrum, is the collective responsibility of all of the team members. In a Scrum team all team members must collaborate and pull together to get the team over the line - so most team members should be able to muck in and assist with most of the tasks the team has before them.
The long term goal of Agile teams is actually to achieve something higher still. Beyond T-shaped people there's discussion about the need for 'broken combs'...
Imagine the teeth of a broken comb with some teeth missing completely and others which are much shorter. The comb's teeth represent skills/functions.
Pieces of broken combs have some breadth, but they also have some depth, to differing degrees, across a number of skill or functional areas. Imagine each person on the team being represented by a small piece of the comb...with a few full length 'teeth' and a few that they are developing. Collect and assemble these different pieces together and you have enough overlap in skills to make a truly cross-functional team.
Agile teams therefore need T-shaped people or 'broken combs' to be truly cross-functional. That is, each team member needs to be a 'generalising specialist' having skills across a variety of skill areas so that they can jump in, get the job done and collectively succeed in the Sprint goal.