What does it mean to refer to some piece of mathematics as "technical"? We often certain pieces of mathematics described as 'technical'. What does that mean?
To be clear, I am not someone who is literally unsure of the English meaning of the word and looking for a simple explanation.
I am more interested to know if there is any agreement among mathematicians about what the word 'technical' actually connotes. Specifically, is it a negative connotation? Do you think to yourself 'oh  no I don't want to do technical mathematics'? Or do you think 'oh it must have lots of computation' or 'lots of new definitions' or... what?
 A: A technical lemma in mathematics refers to something that is needed for a proof but is independent of the proof, and sometimes the subject area, that it is being used for.  Typically it will be highly abstract but will employ mostly elementary machinery, and it will very often serve to move from one thematic portion of the proof to the next in a single statement.
One of the earlier examples of this you may encounter is Young's inequality: let $1/p + 1 /q = 1$ and then
$$ab \leq \frac{a^p}{p} + \frac{b^q}{q} $$
which holds for all non-negative numbers $a,b$.  The proof of this is technical -- there are a few ways to do it, but a common one is by noting that the $\log$ function is concave and this can be re-arranged to take advantage of that.  There is nothing intuitive about this, and at first glance it doesn't look very useful.  However, it is a key element in proving Holder's inequality,
$$\|fg\|_1 \leq \|f\|_p\|g\|_q $$
which turns out to very useful in functional analysis, finite element theory and all kinds of partial differential equation analysis.
A second example would be the lemma concerning re-arrangements of finite sets of numbers in descending order which is used to prove the existence of a locally convex norm (Day's norm) on certain Banach spaces:
Let $s_1 \geq s_2 \geq \cdots \geq 0$ and $t_1 \geq t_2 \geq \cdots \geq 0$ and let $\pi$ be any permutation of the positive integers.  Then 
$$ \sum_{i=1}^\infty s_i t_i - \sum_{i=1}^\infty s_i t_{\pi(i)} = \sum_{i=1}^\infty \left( s_i - s_{i-1} \right)\left( \sum_{j=1}^i t_j - \sum_{j=1}^i t_{\pi(j)} \right)$$
A: In my mind, a technical lemma is something for which you don't have a really good intuitive motivation, that you don't find to be the heart of the argument but that you need for some reason in your proof. Its proof is typically not illuminating.
If you explain a piece of mathematics to someone over coffee, you would say things like "ok, here is the main idea of the argument: [blabla]. Now, you do need a technical lemma that says [xyz], but let's not bother with why that lemma holds"
A: Depending on context, technical also often means (besides what postmortes and Glougloubarbaki say in their answers) something that is swamped with messy details and subtleties. Examples: The two stability of matter papers (1 and 2) by Freeman Dyson and Andrew Lenard are very technical. David Preiss' paper Geometry of measures in R$^n$: Distribution, rectifiability, and densities is very technical.
