Gardner's theory of multiple intelligences (MI) is roughly about the aspects of a person's brain (or perception/expression). When you look at just the theory, well, some people like it, some don't. The point is, it does relate to learning—in an indirect way.
The theory implies that people learn best in different ways. When you say it this way, it sounds like “learning styles,” which is a different thing. So... what is the MI theory good for in the learning context? Saying that “people have different intelligences” sounds abstract; let's try and actually use the MI concept.

I need to explain topic X to different people, each using only one of the multiple intelligences. So...

• The Spatially Intelligent person is good at visualising. Topic X would be best explained as a flowchart, or a set of diagrams, or an infographic.
• A person with Linguistic Intelligence understands words well. A textual description of the topic -- or verbal communication about it -- would suit the purpose best.
• The keyword for the Logical-Mathematical learner is “reasoning.” An explanation of why is important for this person. This can be via a question/answer session between instructor and learner. Or perhaps a step-by-step, methodical explanation.
• For someone with Intrapersonal intelligence, self-reflection works best. (Self-motivated learners are often tapping into this aspect.) In the case of a “how-it-works” explanation, it might be good to get into only a few details, letting the person explore further.
• Interpersonal intelligence implies that learning happens best when a person interacts with other people. Here, the training approach would involve a group session headed by the instructor.
• While “Bodily-kinesthetic” intelligence is about the connection between learning and the body (as in dance), it does carry an element of hands-on learning. Addressing this aspect means facilitating “learning by doing.”

Where the MI theory doesn't make sense for learning is that, well, you can't think of your learner as one type. You can't do any learning design by looking at what the theory says. What the multiple-intelligences theory does tell you is that, you can learn about your learner by trying different ways to get your point across.