These are either terms unique to science or terms that mean something different in science than they do colloquially (in which case, make sure not to use it unless you mean it scientifically!) It's biased towards neuroscience / psych terms, since that's my area, and general terms.
PI - this is one of the oddest terms I've encountered because it's ubiquitous in science but no one anywhere else has heard of it. It means "Principal Investigator" and designates the head of the lab. This is your professor / supervisor who applies for money to run the lab, who determines what you study, and is the boss of the unit called the laboratory.
Lab - short for "laboratory", but no one uses the word "laboratory". Labs include the PI, and 1-30 other people usually (labs can be bigger in industry, but those get subdivided). Most labs have about 5-12 people. Labs include the PI, post-docs, graduate students, research technicians / lab assistants, and undergrads. The post-docs and graduate students (and sometimes the undergrads) have their own projects and usually the projects are related by topic within the lab. The degree of congeniality between lab members differs based on lab culture, which is a function of both PI expectations and individual members of the lab.
Lab Tech / RA - These stand for "laboratory technician" and "research assistant". These terms are sometimes interchangeable and sometimes mean different things within a lab. Usually they refer to the one- to two-year position where a student with an undergraduate degree is doing all of the lab's administrative work and some independent research to gain experience before applying to graduate school.
Post-doc - Post-doctorate researcher. They have already received their doctorate award, aka their PhD.
PhD - this is the degree needed to secure the "Dr." next to your name—it is primarily a research degree usually lasting between 5-7 years in the US (3-4 in the UK). It usually comes with teaching responsibilities and coursework during the first two years.
Grad student - graduate student—student who is in the process of acquiring their PhD.
Undergrad - undergraduate student—student who is in college.
Significant - short for "statistically significant", usually meaning the p-value / p-statistic is less than .05, unless the target p-value is otherwise specified. (P-values are a statistical measure most commonly associated with t-tests, but they can be acquired from Frequentist statistical tests in general.) Don't use this word unless you're referring specifically to a result in comparison to its p-statistic.
Noise - this often refers to statistical noise; values that don't correlate with anything and that add useless "noise" to a clear signal. (This is not a technical definition; check Wikipedia for that :)).
Correlation - how much two variables relate to each other. Regression is how well you can predict how variables will interact. Visual pictures of this helps a lot, and examples… you'll get these in your stats class :).
Bio / Chem / Orgo / Physics / Math / Psych / PChem / Neuro - class abbreviations: biology, chemistry, organic chemistry, physics, math, psychology, physical chemistry, neuroscience…
The Literature - all scientific papers that have been written on a subject
PubMed / Web of Science / Google Scholar - databases for retrieving papers
Cosyne / NIPS / SfN / etc… - Names of neuroscience conferences. There are a lot of conferences out there, and you'll get to know the ones in your field and area of the world.
Nature / Science / Nature Neuro / Cell / PNAS / PLOS ONE / Journal of Vision - common journal names I encounter; again, you'll learn the common journals (and their rankings) in your field as you go along.
NSF / NIH - two of the US's largest funding agencies. PIs will talk about these. If you hear students talking about the NSF grant, they're referring to the NSF Graduate Research Fellowship Program grants, which fund graduate students for 3 years and are quite prestigious.
NSF / Beckman / Hertz / Goldwater / NDSEG / Mellon-Mays / HHMI / … - undergraduate and graduate research fellowhips
REU - undergraduate research experience. Paid scholarships to do research for the summer, usually between 35-40 hours per week.
Pre-med - undergrad studying to go to medical school. Pre-meds often have to do research to get into medical school, but they have a reputation for treating research differently than students who wish to pursue PhDs (pre-PhDs do not have a common term. Pre-grad is sometimes used.)
More to come!